Question: Geoff and Trevor each roll a fair six-sided die.  What is the probability that the product of the numbers they roll is even?
Explanation: There are $6 \times 6 = 36$ possible outcomes.  The only way that they can roll an odd product is if both their rolls are odd.  Since 3 of the 6 faces on each die are odd, this can occur in $3 \times 3 = 9$ ways.  So a even product can occur in $36-9= 27$ ways, and the probability is thus $\dfrac{27}{36} = \boxed{\dfrac34}$.